Abstract
Provided that vehicles are riding with constant velocity, the mean value of the car driving force needed to compensate energy dissipation through the wheel damping, is calculated. For suitably strong harmonic road excitations, there are two stable and one unstable velocity near the critical speed of the car. This behavior is extended to the case of stochastic roads that shows corresponding effects when the calculated mean driving force is plotted versus the constant car velocity. More important is the inverse case that the driving force of the car is fixed by means of a suitable control meanwhile the car velocity is variable and fluctuates around a stationary mean value. For small car damping and narrow-banded road profile, a further acceleration of under-critical car velocities is no longer possible because of the blockade by the resonance characteristic. The car velocity finally jumps to much higher speeds when the driving force is strongly reinforced in order to pass over the resonance peak. This behavior is investigated for stochastic road profiles described by new second order filter equations under additive white noise applied to the across and along dynamics of quarter car models. To clarify main original contributions, this paper presents first investigations of the along dynamics of quarter car models applying a new nonlinear first order car equation which is strongly coupled through randomly fluctuating car velocities with the second order road and car equations of the vertical road and car displacements, respectively. The associated systematic behavior is numerically investigated by means of covariance equations showing jump phenomena of the mean car velocity that corresponds to the Sommerfeld effect, well-known in rotor dynamics.
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References
Arnold L (1974) Stochastic differential equations. Wiley, New York
Wedig WV (2003) Dynamics of cars driving on stochastic roads. In: Spanos PD, Deodatis G (eds) Computational stochastic mechanics. Millpress, Rotterdam, pp 647–654
Kloeden P, Platen E (1992) Numerical solution of stochastic differential equations: a review. Springer, Berlin/Heidelberg
Popp K, Schiehlen WO (1993) Fahrdynamik. Teubner-Verlag, Stuttgart
Sobczyk K, MacVean DB, Robson JD (1977) Response to profile-imposed excitation with randomly varying transversal velocity. J. Sound Vib 52(1):37–49
Davis BR, Thompson AG (2001) Power spectral density of road profiles. Veh Syst Dyn 35(6):409–415
Doods CJ, Robson JD (1973) The description of road surface roughness. J Sound Vib 31:175–183
Wedig WV (2014) Velocity Controlled ride of vehicle systems on rough roads with randomized surfaces. In: Proceedings of the 8\(^{\rm th}\) European nonlinear dynamic conference, ENOC 2014, 6–11 July, Vienna
Di Paola M, Pirrotta A (2001) Time delay induced effects on control of linear systems under random excitation. Probab Eng Mech 16(1):43–51
Solodovnikov VV (1960) Introduction of the statistical dynamics of automatic control systems. Dover Publications, New York
Von Wagner U (2004) On nonlinear stochastic dynamics of quarter car models. Int J Non-linear Mech 39:753–765
Litak G, Borowiec M, Frisell MI, Przystupa W (2009) Chaotic response of a quarter car model forced by a road profile with a sochastic component. Chaos Solitons Fractals 39:2448–2456
Wedig WV (2012) Simulation of road-vehicle systems. Prob Eng Mech 27(1):82–87
Wedig WV (2014) Bi-linear simulation schemes applied to multi-body vehicles riding on randomly profiled road surfaces. In Lemaire M, Souza de Cursi E (eds) Proceedings of the 2nd international symposium on uncertainty quantification and stochastic modeling, 23–27 June, 2014, Rouen, France, hosted by Insa-Rouen
Wedig W (2015) Jump phenomena and bifurcations in stochastic vehicle-road dynamics, survey lecture in section 15 on applied stochastics presented at the 86th annual meeting of international association of applied mathematics and mechanics, 23–27 March, 2015, Lecce, Italy, to be published electronically in PAMM (Proceedings in Applied Mathematics and Mechanics)
Wedig WV (2015) New resonances and velocity jumps in nonlinear road-vehicle dynamics, to appear in the booklet of abstracts, IUTAM symposium on analytical methods in nonlinear dynamics, Frankfurt, 6–9 July, 2015
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Wedig, W.V. Jump phenomena in road-vehicle dynamics. Int. J. Dynam. Control 4, 213–220 (2016). https://doi.org/10.1007/s40435-015-0182-1
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DOI: https://doi.org/10.1007/s40435-015-0182-1